Intelligence model on sequence-based prediction of PPI using AISSO deep concept with hyperparameter tuning process

Protein–protein interaction (PPI) prediction is vital for interpreting biological activities. Even though many diverse sorts of data and machine learning approaches have been employed in PPI prediction, performance still has to be enhanced. As a result, we adopted an Aquilla Influenced Shark Smell (AISSO)-based hybrid prediction technique to construct a sequence-dependent PPI prediction model. This model has two stages of operation: feature extraction and prediction. Along with sequence-based and Gene Ontology features, unique features were produced in the feature extraction stage utilizing the improved semantic similarity technique, which may deliver reliable findings. These collected characteristics were then sent to the prediction step, and hybrid neural networks, such as the Improved Recurrent Neural Network and Deep Belief Networks, were used to predict the PPI using modified score level fusion. These neural networks’ weight variables were adjusted utilizing a unique optimal methodology called Aquila Influenced Shark Smell (AISSO), and the outcomes showed that the developed model had attained an accuracy of around 88%, which is much better than the traditional methods; this model AISSO-based PPI prediction can provide precise and effective predictions.

www.nature.com/scientificreports/encounter time and expense constraints and cannot match the demands of human life scientific studies as in the post-genomic age.Also, it is profitable to mention that the presence of subjective or objective variables, including activity as well as experiment error, causes experimental findings to diverge significantly from the actual outcomes, occasionally resulting in a high fraction of false-positive and maybe even false-negative experimental findings [11][12][13][14][15][16][17][18] .
A common method for determining the most discriminative features for multi-class classification is linear discriminant analysis (LDA).Deep recognition models have performed remarkably over the last ten years 19,20 .Except for the yeast, wherein diverse characteristics have been extensively investigated, amino acid sequence-dependent predictors constitute a large proportion of the publications on computationally anticipating proteome-wide PPIs.Features derived from amino acid sequences and their physicochemical qualities are used in sequence-dependent predictors.Auto covariance (AC), conjoint triads (CT), and pseudo amino acid composition (PSEAAC) were examples of feature models that have frequently been employed for predicting PPIs 21,22 .
Traditional biophysical approaches for PPI detection are both time-consuming and costly.Conventional computational strategies, on the other hand, demand prior knowledge of genomic and phylogenetic schematics and sequence interpretation to produce acceptable PPI predictive performance 23 .Machine learning (ML) approaches, such as Artificial Neural Networks (ANN) 24 , Support Vector Machines (SVM) 25 , and deep learning 26,27 , provide critical means for prudent prognosis of PPIs premised on the straightforward derivation of protein data from amino acid sequences, demonstrating that deep-learning systems can manage huge raw as well as complicated information and effortlessly learn beneficial and much more conceptual features in the task of PPI prediction.As a result, we created an AISSO-based deep concept with a hyperparameter tuning approach for accurate and reliable PPI prediction.This work's notable contributions have been listed below.
• We created an enhanced semantic similarity-based feature in the feature extraction process along with other features, which will aid in obtaining accurate findings.• To provide an accurate forecast, an Improved RNN is developed to ensure the minimization of loss.
• A unique Aquila Influenced Shark Smell optimization is created to adjust the two classifiers' weights, which shows efficient prediction.
The coordination of this article is as follows.Section "Literature survey" offers a synopsis of prior works on PPI prediction, Section "Problem statement" explains the problem statement of the research, Section "Proposed method" describes our suggested method for AISSO PPI prediction that is sequence-dependent, Section "Results and discussion" illustrates the results of the experiments, and Section "Conclusion" concludes the work, and the following section lists references.

Literature survey
Some of the works related to PPI prediction were briefly reviewed in this section.
Patrick et al. 28 created a computational strategy for developing precise protein complex structures.In this case, the AlphaFold2 is being used to forecast heterodimeric protein complexes.Models are created by using AlphaFold2 methodology and optimized multi-sequence alignment.A simple formula was built utilizing the projected interfaces to predict the DockQ score, separating satisfactory from wrong designs and associating noninteracting proteins with state-of-the-art accuracy.Even though this approach can yield excellent predictions, it only addresses protein complex structures in their heterodimeric form, even though every protein chain in such complexes might also have homodimer topologies or even other higher-order modes.
Satyajit et al. 29 developed the AVPSO approach for PPI prediction, which is utilized to choose the optimum collection of features.The ideal feature subset gets utilized to forecast the PPIs by employing the light gradient boosting machine (LGBM) algorithm.This suggested model AVPSO-LGBM attained around 97% accuracy rate as well as around 95% in the fivefold CV assessment.The AV-PSO-LGBM beats conventional methodologies regarding prediction accuracy, indicating its generalization capabilities.
DeepTrio, a sequence-dependent strategy for predicting PPI utilizing mask multi-parallel CNNs, was reported by Xiaotian et al. 30 .DeepTrio offers improved PPI prediction and an understandable depiction of the significance of every protein sequence in both online and offline implementations.DeepTrio is being upgraded to give further perspectives on the influence of every input node on prediction outcomes.
Yang et al. 31 established multiple modal protein pre-training paradigms with three modes: sequence, structural, as well as function (S2F).Interestingly, this approach encodes the structural characteristic using the topological complexity of heavy atom point clouds.It enables the system to gain structural data regarding the backbones and branched chains.Furthermore, this approach integrates information from the operational descriptions of proteins acquired from research or hand annotations.The experimental outcomes reveal that the S2F trains protein embeddings and works well on a multitude of PPI tasks.
Chiara et al. 32 developed a revolutionary technique that was applied in a publicly accessible tool, "Pep-Threader, " to anticipate and analyze PPIs.PepThreader threads numerous segments produced from a full-length protein sequence over a secondary peptide template combined with a target protein, "spotting" promising linking peptides and rating it on a threading score (TS) that depends on structure and sequence.The TS process begins with a scoring system that depends on the sequence resembling peptides.Following that, the original hits are reranked utilizing structure-dependent scoring methods.
Bin et al. 33 34 suggested SDNN-PPI, a PPI forecasting methodology built on self as well as deep learning.To more precisely forecast PPIs, this tactic employs self-attention to optimize DNN feature retrieval.There was a fivefold CV to assess the generalization capabilities of SDNN-PPI.The one-core and crossover networks are used extensively to assess the model's merits and drawbacks and forecast PPIs.The findings also revealed that the system appropriately forecasts the interaction pairings in the network.
Zeng et al. 35 created Deep PPISP, a unique deep learning-dependent system for PPI site prediction that blends local contextual and global sequence information.A sliding window was utilized to collect characteristics of neighbours of a target amino acid for local contextual information.A text CNN model is being used to retrieve features from the entire protein sequence for global sequence characteristics.Then, the local contextual and global sequence information are integrated to anticipate PPI sites.
Wu et al. 36 have deployed more insightful feature extraction made possible by this module's effective capture of pertinent patterns and representations found in protein sequences.To ascertain the relationships between pairs of input proteins, the paper built a novel FRN that was incorporated into our model's Global Feature Extraction module.The FRN efficiently captures the underlying relational information between proteins by enhancing PPI predictions.In sequence-based PPI prediction, the DL-PPI framework exhibits cutting-edge performance.
Valverde et al. 37 have introduced a brand-new deep learning framework called DPPI that can be used to model and forecast PPIs using sequence data.Our model effectively uses evolutionary information of a protein pair under prediction as well as existing high-quality experimental PPI data, combining a deep, Siamese-like convolutional neural network with random projection and data augmentation to predict PPIs.According to our experimental data, DPPI performs more computationally efficiently and beats state-of-the-art approaches on some benchmarks regarding the area under the precision-recall curve.
Jha et al. 38 have exploited the structural information and sequence properties of proteins; we apply a graph convolutional network (GCN) and graph attention network (GAT) to predict the interaction between proteins.We construct protein graphs using the PDB files, which include three-dimensional atomic coordinates.The protein graph represents the residue interaction network, sometimes called the amino acid network, in which every node is a residue.They are connected if two nodes contain two atoms (one from each node) inside the threshold distance.We employ the protein language model to extract the node/residue features.The protein sequence serves as the language model's input, while the feature vectors for each amino acid in the underlying sequence serve as its output.Table 1 shows the reviews of conventional models.

Problem statement
A living thing's necessary component is protein.Predicting PPIs significantly affects illness prevention, medicine development, and our comprehension of life's behavioural processes.While the advancement of high-throughput technology allows for identifying PPIs in large-scale biological research, time, cost, false positive rate, and other constraints limit the extensive application of experimental approaches.To predict PPIs quickly and reliably, computational methods are therefore desperately needed as a supplement to experimental methods.
Class imbalance occurs when there are significantly fewer interacting protein pairs than non-interacting pairs in PPI datasets.Extracting meaningful information from protein sequences without overfitting or losing information is difficult.It is still difficult to interpret the predictions of sophisticated deep learning models, particularly in biological applications where interpretability is crucial for experimental validation and advancement.The model must function effectively on unknown proteins and interactions for practical use.Although many elevated experimental methods have been created to predict the PPIs, those have limitations like high cost and time consumption, and the selected features and classifiers are inappropriate and inefficient.However, the protein interaction found by experimental methods can only account for a small portion of the entire PPI

Proposed method
Protein-protein interaction (PPI) prediction was important for understanding biological activities.Even though many different types of data and machine learning technologies have been employed in PPI prediction, effectiveness still has to be improved.Consequently, this paper presents a unique PPI prediction approach with two working phases: feature extraction and prediction.In the first phase, in addition to the traditional characteristics such as sequence-dependent and Gene ontology, we produced additional features using the semantic similarity approach, which would aid in accurate prediction.AISSO neural networks such as DBN and upgraded RNN were used in the second stage for better prediction.In addition, a unique optimization termed Aquila Influenced Shark Smell was developed in this work to provide a better and more reliable prediction by optimizing the weighting parameters.Figure 1 depicts the architectural design of the proposed PPI prediction approach, and a thorough description of our proposed work follows.

Feature extraction
This work extracted three features from the given inputs: sequence-based physicochemical features, Gene Ontology (GO) based features, and semantic similarity-based features.A brief description of the feature extraction process is given below.

Sequence-based physicochemical features
The proteins have been utilizing twelve physical and chemical characteristics within its combined amino acids as the principle for PPI prognostication: hydrophilicity, adaptability, convenience, turn the scale, external surface, polarizability, antigenic tendency, hydrophobicity, net charge indicators of the side chains, polarity, solvent obtainable surface region, as well as side-chain volume.Hydrophobicity and polarity were the 12 qualities assessed on two distinct scales.The scores of the twenty critical amino acids' physical-chemical property scales are listed in 35 .Every amino acid gets converted into a vector of 14 numerical data, one for each physicochemical scale rating.Because proteins fluctuate in length, they could be depicted by a varying count of vectors.
Alternatively, classification within an ensemble Meta-learning, including an ANN, k-NN, or NB, demands consistent feed.To generate a unified feed for the learner's classification of the ensemble meta-base, the protein description is converted in a consistent vector form with auto-covariance (AC), whereby all proteins having different quantities of amino acids get portrayed by the identical length vectors.The AC of a protein sequence's physicochemical characteristic scale describes the average correlations among amino acids split by a specific spacing over the complete protein sequence.This spacing between an amino acid and its neighbour is indicated here as a specific count of residues.The l th physical-chemical property scale's AC for protein P, AC l,g is given by where g is the preset gap, L is the P's length,γ l is the average of the l th physical-chemical scale values for P. By defining the maximum range to G i.e.g = 1, 2, 3, ..., G , every protein may be initialized of k × GAC elements, where k seems to be the physicochemical property scales count.
Original physicochemical scale data is converted into a unified vectorial format utilizing AC between amino acids.Consequently, irrespective of length, every protein may be described by the same length vectors.Despite their varied lengths, proteins P1 and P2 were expressed by vectors of 28 AC values.To eliminate variance impacts, set the mean of every feature to zero standard deviation to one, as shown below: where S l denotes the normalized value, α l represents the raw value of the l th AC, γ l and SD l represents the mean as well as the standard deviation of the l th AC, while M denotes the multitude of AC values inside the AC vector.
Furthermore, we have used a min-max scaling approach to scale the normalized AC values to a predetermined range of [0, 1] to guarantee that the ACs produced via diverse physical chemical scales were proportionate and will lessen the effect of outliers even more.Equation (4) describes the min-max scaling.
where Scale l seems to be the scaled value, S l represents the l th AC's standardized value,MAX l as well as MIN l were the maximum as well as a minimum of the l th AC's standardized values, respectively.
(1) www.nature.com/scientificreports/Gene ontology (GO) feature extraction GO seems to be a systematic vocabulary for identifying gene functionalities, including their links to molecular functioning, cellular elements, and biological processes.Each subontology would be expressed as a grounded DAG, in which Every link indicates a connection of two contexts (part_of, is_a), and every node correlates to a GO-term.This hierarchy helps understand operational interactions among genes and has been highly beneficial in appraising the significance of genes' involvement in diverse biological processes, notably PPI prediction.
We have used a method that classifies protein pairings by clustering GO terms.We explore the GO hierarchy from the GO terms in G u as well as G v up to their lowest common ancestor (ULCA), two given sets of GO terms G u , and G v tagging each of the proteins p u as well as p v in a pair.In this way, we may determine the LCA of every protein pairing < p u , p v > in a specified collection of protein pairings.The identified LCAs are stored in a list sorted according to hierarchical GO levels.Except for those already assigned to a pre-existing cluster, each LCA was regularly aggregated in the set of sorted lists to create a cluster.Consequently, the entire GO-terms DAG is split into a set of mutually exclusive subgraphs anchored by an LCA.
GO-term feature vectors were created by assessing the existence or non-presence of common GO words or by assigning them a weight based on the local topology and the data they contain.Alternatively, one GO-dependent feature is defined as a GO group referenced by LCA.To convert these annotated groups G u and G v for every protein pairing < p u , p v > into GO-based numerical values that LCA indexes, initially find the GO terms in sets G u as well as G v on every LCA-indexed subgraph.We calculate the nodes along the rising route up to the base of a subgraph for every GO term and add the node numbers on the subgraph.The value of the matching GO term feature gets allocated to this sum.

Improved semantic similarity based feature extraction
When annotations were plain texts, syntactic similarity alone cannot determine the proximity between sources.Tags generally struggle with heterogeneity as well as ambiguous issues, in which taggers may use multiple words with identical meanings or even the same word with distinct meanings.As a result, while comparing and identifying resemblance, SSD retrieves semantic relations.The degree of similarity has been calculated using the Semantic Similarity Identification approach.Each source is mapped to compute the similarity.Specifically, the vector model suffers from problems including missing semantic data and word impropriety (e.g., ignore synonymy).The PWR approach eliminates vector semantic issues by integrating symbolic features into the matrix form.The SSD approach's main focus in this application is to use a cosine similarity measure to identify the relationships between each pair of resources.SSD cosine similarity incorporates both syntactic and semantic similarity.
In this work, the improved semantic similarity is used to know the relation between two GO terms (R a , R b ).ω a is the weight generated for each protein sequence.The weight is calculated using the cubic map function.This improved semantic similarity method was utilized in this work to obtain the best and most appropriate features.

Prediction phase
The prediction model applies the retrieved characteristics and uses a hybrid model incorporating the classifiers from Deep Belief Networks and Improved Recurrent Neural Networks.Figure 2 shows the prediction phase model.The idea behind the hybrid is as follows: The characteristics are first passed to each of the two classifiers individually, and the final result is determined by averaging the output of the classifiers using modified scorelevel fusion.Here, the suggested AISSO is used to train both classifiers by adjusting the ideal weights, improving the prediction outputs' performance.

Improved recurrent neural network (RNN)
RNNs are a kind of neural net wherein the links between functional blocks create a circle.Except for feedforward networks, RNNs may handle arbitrary sequences of inputs utilizing their internal memory.An RNN's computational units each have a time-dependent actual valued activation and a configurable weight.RNNs were  8) to specify the values of their concealed blocks.
The learned architecture still has an identical input size because RNN has been defined from the perspective of migration from one stage to another.Furthermore, the design utilizes a unique transitional formula having identical attributes for every time interval.Long Short-Term Memory (LSTM) is another RNN in which LSTM cells substitute the classic hidden layers.Those cells were composed of multiple gates that could govern the input stream.An LSTM cell has four gates: input gateway, cell state, forget gate, and output gate.This has a sigmoid tier, a tanh layer, and point-wise multiplication.The following were the multiple gates as well as their operations: • Input gate: This input gate is generally comprised of inputs.Some retrieved characteristics would be utilized as input in our work.• Cell State: The system runs throughout and has gates allowing it to add and remove data.
• Forget gate: Specifies the level of knowledge that'll be permitted.
• Output gate: LSTM's output makes up this component.
• Integers from 0 to 1 are output by the sigmoid layer, indicating how much of each component can move.
• A new vector created by the Tanh layer is added to the state.
The cell status gets modified depending on the gate output.The accompanying formulas have been used to express it mathematically.where x t seems to be the input vector,H t indicates the vector of output, e t would be the cell state vector, F t is the vector for the forget gate, i t is the vector for the input gate, q t has been the vector for the output gate, while W, d has been the parameter weight matrix and vector.The tanh activation function, which is represented in this paper, is W hh denotes the recurrent neuron weight and W xh denotes the input neuron weight.The loss function measures the difference between an algorithm's current and predicted output, assessing data mimicry.Cross-entropy is commonly used in machine learning for more robust generalization models and faster training.With binary and multiclass categorization issues, cross-entropy could be applied.
A binary regression model may be utilized to categorize observations into two groups.Particularly a vector of input characteristics x, the model's output for a provided observation may be read as a probability that offers the foundation for categorizing the observation.The logistic function Q(ε) = 1 (1+e −ε ) is being used to describe the likelihood in a logistic regression, wherein z represents a function of the input vector ε , most frequently a linear function.Throughout most instances, logistic regression improves the log loss for all of the findings on which it is trained, which is identical to maximizing the sample's average cross-entropy.For example, suppose we have N samples with each sample indexed by n = 1, 2…N.The average of the loss function is then given by where ẑn = h(w.χn ) = 1 (1+e −w.χn ) Cross-entropy loss is another name for logistic loss.It is sometimes referred to as log loss.This work uses the cross-entropy loss function below to lessen the model's loss.

Deep belief network
DBNs appear to be inventive techniques.A DBN is composed of stacked RBMs that engage in greedy application training to achieve good performance in an unsupervised environment.Training took place layer-by-layer in a DBN, executing each layer as an RBM trained on top of the previous layer.As a feed-forward network that allows for weight fine-tuning using an alternative strategy, DBNs are a group of RBM layers used for pre-training.
(8) www.nature.com/scientificreports/Since RBMs and auto-encoders can be pre-trained on unclassified data and fine-tuned on a small quantity of labelled data, their significant utilization is probably due to the lack of labelled data.A DBN was trained layer by layer using a greedy application training technique.It was used because the greedy application method optimizes each layer at a time in a greedy manner.A joint supervised training algorithm is typically applied to each layer during the fine-tuning stage that follows unsupervised training.
A greedy tier unsupervised approach was used in the pre-training phase to train the basic features, and a softmax layer was added to the top layer during the fine-tuning phase to improve the characteristics of the labelled samples.As shown in Eq. ( 17), the SD was normalised to graphically depict the complexity.
In this, v is each visible unit of RBM, while h is each hidden unit.The model's three metrics were found to select the strategy.:φ= {U, �, D} .The weight matrix U, the hidden layer component bias , as well as the visible layer component bias D.
Consider an RBM comprises of p hidden cells as well as q visible cells, with υ r representing the rth visible unit &ℏ r representing the jth hidden unit, with the attributes stated in Eq. ( 18): Here µ r,j denotes the weighted average of the rth exposed cells, as well as the jth concealed cell from Eq. (19).
Here A r denotes the rth visible cell's bias limit from Eq. ( 20); where C j represents the jth visible cell's bias threshold.The RBM energy formula has been expressed in Eq. ( 21) for (v, h) via the current state, assuming concealed as well as visible layers replicate the Bernoulli distribution.φ = V rj , A r , B j represented the attributes of the RBM prototype, and the operation of energy displayed the value of energy amongst estimations from every viewable node as well as every concealed layer node.Because of the energy function's extension and expansion, the combined probability distribution formula was obtained, wherein the nodes collection of viewable layers as well as hidden layers nodes was in a particular state independently (v, h), as shown in formula ( 22): where Z(φ) the normalized aspect or distributed function displays the overall energy estimates of all available states for the set of hidden nodes and visible layers in the expression (23).The parameters are often obtained by determining the probability function.After presenting the associated likelihood distribution P(v, h|φ ) the margin distributions P(v|φ ) of the viewable layer node collection might be obtained by adding the overall restrictions of the concealed layer node collection in Eq. ( 24): The marginal distributions represent the likelihood that the node configuration inside the visible layers fell within the designated level distribution.The RBM system's extraordinary layer-layer connections and inter-layer connectionless form give it the following noteworthy requirements: The enactment conditions of every hidden layer cell were restrictively autonomous after the presentation of the visible cell circumstances.In this instance, the hidden component's activation probability was as indicated by Eq. ( 25): Consequently, upon stating the hidden components' criterion, the visible components' initiation probability likewise became uncorrelated, as seen by Eq. ( 26): This was necessary to figure out the 3 model parameters before selecting the RBM model:φ = V ij , A r , B j The logarithmic probability measures were used in the parametric organization to determine the parameters' subordinates.According to Eq. ( 24), P(v|φ ) = 1 Z(φ) h e −E(v,h|φ ) , Since energy E was determined by extending ( 17) www.nature.com/scientificreports/P, it would be inversely related to likelihood P. The inclination increase strategy, related to parameter adjustment as shown by Eq. ( 27), was the standard method for increasing functional probability.
This repetitive approach increased the probability P while decreasing the energy E. Table 2 shows the hyperparameters of classifiers.

Modified score level fusion
In score-level fusion, an individual's identity is determined by consolidating the match scores produced by various biometric matches.Usually, the biometric system uses the single scalar score produced due to this consolidation process.The conventional score level fusion is given below.The conventional score level fusion has some limitations.Individual deep-learning models' scores can be susceptible to noise or errors during prediction.These errors can propagate and affect the final fused score, potentially leading to misclassification.To overcome this, we have modified a new method for fusing scores of both deep learning prediction scores.To conventional score level fusion is given in Eq. ( 28), (i) The map of mRNN output prediction is provided in Eq. ( 29) (ii) Also, compute Mape for DBN output is given in Eq. (30).
y i is the actual score, S mRNN is the predicted score of modified RNN (iii) To fuse the score by using Eq. ( 31), where w 1 , w 2 are the weights, these are provided in Eqs. (32)and (33).The weight can be calculated by using the above map values.

AISSO-based optimal training of hybrid classifier
The hunting techniques of eagles, particularly those of the Aquila genus, inspire AOA.Nature-inspired algorithms frequently present creative answers to optimization issues by imitating natural processes.AOA usually strikes a good balance between exploration and exploitation.Analogously to eagles hunting for prey, it uses processes to efficiently explore the search space and capitalize on potential places for better answers.Applications of AOA can be found in many different disciplines, including engineering, finance, logistics, and more, for a wide range of optimization problems.It is appropriate for a wide range of real-world applications due to its versatility.Good convergence properties are frequently exhibited by AOA, which means it can quickly and effectively converge to almost ideal solutions.
For applications that require speed, this efficiency is essential.To attain optimal performance, SSO, like many other optimization algorithms, must have its parameters adjusted.Choosing the right parameter values can be difficult and might require much experimentation.Despite its exploration-exploitation balance, SSO may nevertheless experience the problem of convergent to local optima, particularly in multimodal or highly nonlinear optimization environments.Developing escape strategies from local optima is crucial to enhancing its robustness.
Even though SSO draws inspiration from natural occurrences, its theoretical underpinnings might not be as solid as those of certain more known optimization techniques.Due to this lack of theoretical rigour, its behaviour under certain situations may be more difficult to evaluate and comprehend.The computational needs of SSO may become exorbitant depending on the size and complexity of the task.This could be a disadvantage, especially for real-time applications or large-scale optimization projects requiring much processing power.The combination of SSO and Aquila optimization is the proposed AISSO.SSO algorithm influences the Aquila update.The hybrid optimization idea outperforms the separate algorithms regarding speed and convergence rate.

Objective function and solution encoding
The solution provided as input to the proposed AISSO-based model is shown in the following Fig. 3.
This work aims to minimize mean square errors, as indicated by Eq. (34).Initially, the attributes are provided to each of the two classifiers separately.The outcome is obtained by averaging the classifiers' outputs using modified score-level fusion.
Here, the MSE is the mean square error.The shark smell technique was motivated by the shark's capability to hunt using its keen sense of smell.Several assumptions are taken into account when building the mathematical formulation 39 .They are as follows: (1) A fish gets hurt, so blood is injected into the water (the search space).Consequently, when contrasted to the shark's motion velocity, the wounded fish's velocity may be ignored; in another way, the source (prey) is considered to be set.(2) Blood is injected into the sea in a usual manner.The impact of water movement on odour-distorting particles is overlooked.The odour particles were more significant around the damaged fish.As a result, tracking the odour particles aids the shark in approaching its meal.(3) One damaged fish in the shark's search area resulted in one odour source.

SSO initialization: first odour particles identification
When the shark detects an odour, the search activity starts.In reality, odour molecules from a wounded fish get poor diffusion (prey).A population of starting solutions for an optimization challenge in the viable search space where β ℓ is the level k velocity constraint ratio.Equation ( 42) calculates the value of VV ℓ r,τ that has the identical symbol as the phrase chosen by the minimal operator in Eq. (42).Owing to the shark's forward motion, its updated position I ℓ+1 y was calculated using its prior velocity as well as position.
where �t ℓ is the phase ℓ time interval.For the sake of convenience, �t ℓ is considered to be the same for all phases.Equation ( 42) yields every element of VV ℓ y,τ (τ = 1, ...., ND) of vector VV ℓ y .As the proposed logic, we use the Aquila Optimization's updation function instead of SSO's updation function.The random variables r1 and r2 are created using the random function, while the random variable r3 is generated using the ICMIC map.
When a high soar locates the prey location, the Aquila orbits its prey, positions itself, and then attacks.Contour flying with short glide aSSOult is the name given to this technique.In preparation for such an aSSOult, AO closely investigates the specified region of the intended prey.This behaviour is described numerically as Eq. ( 44).
where X 2 (t + 1) is the outcome of the 2nd search method's subsequent recapitulation of t.The dimension area is D, as well as the levy flight dispersion function is Levy(D A ) , that is the derivative of Eq. (44).At the fth itera- tion,X R (t) is a randomized solution picked in the range of [1 N].where s represents a fixed value of 0.01, RI 1 and RI 2 represents a random integer among 0 & 1, σ would be com- puted with the help of Eq. ( 45).
where β is a fixed to 1.5.In Eq. ( 44), The values of y and x, which have been ascertained as follows, indicate the spiral pattern in the search.
where ϒ seems to be a small number with a value of 0.00565.D A1 is an integer array that starts at one and moves to the search space length (Dim), and ω will be 0.005.The best shark positions were then chosen based on the greatest OF value.
In this study, Gauss mutation is used to provide a precise and trustworthy optimization.Gaussian mutation works by simply adding a random value from a Gaussian distribution to each vector member of an individual to create a new generation.Table 3 shows the optimization parameters.

Results and discussion
This section covers the results and discussion.

Simulation setup
The MATLAB tool has been used to implement the proposed work.In this research, two datasets were employed.The AISSO-based PPI prediction algorithm we have presented has been analyzed and its performance matrices compared with traditional methods like Aquila 45 , Cat Swarm Optimization (CSO) 46 , Hunger Games Search (HGS) 47 ,Poor Rich Optimization (PRO) 48 , and Shark Smell Optimization (SSO) 49 .

Analysis of accuracy
The projected model's performance is evaluated for E. Coli and S. Cerevisiae using different learning percentages, namely 60, 70, 80, and 90.According to the findings collected, the projected model has achieved the maximum accuracy for varying learning percentages compared to the conventional models.The obtained results are illustrated in Fig. 7.At 60 percent of the learning percentage, the developed model has attained enhanced accuracy (~ 87.37), which is much better than the conventional approaches such as Aquilla, CSO, HGS, PRO and SSO,

Local and global optima analysis
An extrema (highest or minimum) point of the objective function for a specific area of the input space is known as a local optimum.The maximum or lowest value the objective function can accept throughout the whole input space is known as the global optimum.The global optimum is best for the system's overall performance, whereas the local optimum is best for the performance of a single component.Figure 8 shows the local and global optima.
Finding the minimum or maximum over the specified set, as opposed to local minima or maxima, is how global optimization differs from local optimization.Using traditional local optimization techniques, determining an arbitrary local minimum is quite simple.

Fig. 7 .
Fig. 7. Comparison of the proposed AISSO-based PPI prediction approach with traditional optimization algorithms (a) E. Coli and (b) S. Cerevisiae.

Table 1 .
Reviews of conventional models.networks because biological experiment methods are expensive and time-consuming.Furthermore, the detection results may have false positives and negatives due to the experimental setup and operational procedures.Thus, it is essential from a practical standpoint to create trustworthy computational techniques for reliably predicting protein interactions.

Table 2 .
Classifier Hyper-parameters.This improved score level fusion technique was used to identify which deep model achieves a better prediction rate than others.Based on the minimum mape weight-based fusion technique to fuse the score accurately.This modified fusion technique can be tailored for improved performance.

Table 4 .
Performance comparison of our proposed AISSO strategy with E. Coli for diverse scenarios.

Table 5 .
Performance comparison of our proposed AISSO strategy with S. Cerevisiae for diverse scenarios.

Table 6 .
Statistical analysis of our proposed AISSO-based strategy vs. other optimization algorithms for E. Coli.

Table 7 .
Statistical comparison of our proposed AISSO-based strategy to extant optimization algorithms for S. Cerevisiae.respectively for E. Coli.Also, based on the accuracy of the developed model for S. Cerevisiae at LR 80, the developed model obtained the highest accuracy compared to the traditional methods.

Table 8 .
Analysis of computational time.